405 research outputs found
Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
Finsler and Lagrange spaces can be equivalently represented as almost Kahler
manifolds enabled with a metric compatible canonical distinguished connection
structure generalizing the Levi Civita connection. The goal of this paper is to
perform a natural Fedosov-type deformation quantization of such geometries. All
constructions are canonically derived for regular Lagrangians and/or
fundamental Finsler functions on tangent bundles.Comment: the latex 2e variant of the manuscript accepted for JMP, 11pt, 23
page
Higher order relations in Fedosov supermanifolds
Higher order relations existing in normal coordinates between affine
extensions of the curvature tensor and basic objects for any Fedosov
supermanifolds are derived. Representation of these relations in general
coordinates is discussed.Comment: 11 LaTex pages, no figure
Перспективи енергетичного співробітництва України та США. (The prospects of energy cooperation between Ukraine and the USA.)
У статті висвітлено історію становлення та перспективи розвитку українсько-американських відносин в енергетичій сфері як один із пріоритетів зовнішньої політики України.
(This article investigates the history of the formation and prospects of Ukraine-US relations in the energy cooperation as one of the priorities of Ukraine’s foreign policy.
Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
We provide a method of converting Lagrange and Finsler spaces and their
Legendre transforms to Hamilton and Cartan spaces into almost Kaehler
structures on tangent and cotangent bundles. In particular cases, the Hamilton
spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on
effective phase spaces. This allows us to define the corresponding Fedosov
operators and develop deformation quantization schemes for nonlinear mechanical
and gravity models on Lagrange- and Hamilton-Fedosov manifolds.Comment: latex2e, 11pt, 35 pages, v3, accepted to J. Math. Phys. (2009
Gauge Theories in Noncommutative Homogeneous K\"ahler Manifolds
We construct a gauge theory on a noncommutative homogeneous K\"ahler
manifold, where we employ the deformation quantization with separation of
variables for K\"ahler manifolds formulated by Karabegov. A key point in this
construction is to obtaining vector fields which act as inner derivations for
the deformation quantization. We show that these vector fields are the only
Killing vector fields. We give an explicit construction of this gauge theory on
noncommutative and noncommutative .Comment: 27 pages, typos correcte
Symplectic geometries on supermanifolds
Extension of symplectic geometry on manifolds to the supersymmetric case is
considered. In the even case it leads to the even symplectic geometry (or,
equivalently, to the geometry on supermanifolds endowed with a non-degenerate
Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is
proven that in the odd case there are two different scalar symplectic
structures (namely, an odd closed differential 2-form and the antibracket)
which can be used for construction of symplectic geometries on supermanifolds.Comment: LaTex, 1o pages, LaTex, changed conten
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